Question

Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9 inches and 64.0 inches.

0.0424

0.1739

0.9318

0.7248

Answer 1

thoughts?

we can do a quick sketch of the situation:

Answer 2

we want to know the area between the two values 64.0 and 62.9

notice how, if you subtract (red area) - (blue area) you get the area in between

therefore, you need to find the z-scores corresponding to 64.0 and 62.9, convert them to probabilities, then subtract the two probabilities

as a reminder:

z-score = (x - mean)/(standard deviation)